Problem 340 In the following exercises, solv... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 340

In the following exercises, solve the equation. Then check your solution. $$ -9.1 n=-63.7 $$

Short Answer

Expert verified

n = 7

Step by step solution

- Isolate the variable

To isolate the variable , divide both sides of the equation by -9.1.\[ -9.1n = -63.7 \]\[ n = \frac{-63.7}{-9.1} \]

- Perform the division

Perform the division to solve for :\[ n = \frac{-63.7}{-9.1} = 7 \]So, $ n = 7 $.

- Check the solution

Substitute $ n = 7 $ back into the original equation to verify:\[ -9.1(7) = -63.7 \]\[ -63.7 = -63.7 \]The solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables

Isolating variables is a key step in solving linear equations.
The goal is to get the variable by itself on one side of the equation.
This helps you solve for the variable's value.
In our example, the equation is \[ -9.1n = -63.7 \].
To isolate '', we need to remove the -9.1 that is multiplying it.
This is done by dividing both sides of the equation by -9.1.
Remember, whatever operation you do to one side, must be done to the other side as well to keep the equation balanced.
After this step, the equation becomes \[ n = \frac{-63.7}{-9.1} \]. Now, '' is isolated, and we can move on to finding its value.

Division in Equations

Division is often used to solve equations, especially when isolating a variable.
In our example, after isolating 'n', we perform the division \[ n = \frac{-63.7}{-9.1} \].
Dividing -63.7 by -9.1 results in 7.
Therefore, \[ n = 7 \].
When dividing with negative numbers, remember that dividing two negatives gives a positive result.
This is why our answer is positive 7.
Always double-check your division to ensure accuracy.

Checking Solutions

Checking your solution verifies that your answer is correct.
Substitute the variable back into the original equation.
In our example, we substitute \[ n = 7 \] back into \[ -9.1n = -63.7 \].
This gives \[ -9.1(7) = -63.7 \].
Simplifying this, we get \[ -63.7 = -63.7 \], which is true.
Hence, our solution \[ n = 7 \] is correct.
Always check your solution to catch any possible mistakes.
It's a good habit that ensures the accuracy of your answers.

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91影视

In the following exercises, solve the equation. Then check your solution. $$ -9.1 n=-63.7 $$

Short Answer

Step by step solution

- Isolate the variable

- Perform the division

- Check the solution

Key Concepts

Isolating Variables

Division in Equations

Checking Solutions

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